1. Field of the Invention
The present invention relates to electronic device modeling systems and, more specifically, to a system for modeling ground plains used in circuit boards.
2. Description of the Related Art
A high-performance digital or mixed signal system can contain thousands of signal lines that must be routed on several layers in the package and printed circuit board (PCB). These signal layers must be placed between or over power and ground planes in order to have an impedance controlled board including microstrip or stripline transmission lines. A power or ground plane also prevents any coupling of signal lines in an upper layer to signal lines in a lower layer. As a result of this, many power and ground layers have to be included in the stack-up. In order to reduce the parasitic effects of the power delivery network (e.g., to reduce the inductance of the planes), these layers can be allocated to power and ground in an alternating manner such that multiple plane pairs can exist in a package or board.
Power and ground planes in electronic packaging can be a major factor for noise coupling. There can be noise coupling not only in the transversal direction between two planes, but also in the vertical direction from one plane pair to another through the apertures and via holes. Excessive supply voltage fluctuations cause signal integrity (SI) problems. In addition, noise voltage that gets coupled to the edge of the board may cause significant electromagnetic interference (EMI). Hence, an accurate modeling of power/ground planes is critical to estimate the noise levels especially in mixed-signal systems where high isolation levels are required.
A solid plane made of a perfect conductor of infinite lateral dimensions would completely shield the fields on one side from the other side. Therefore, there would be no need to consider multiple plane pairs. In reality, however, planes at the same dc level have to be connected with vias to each other in order to reduce the effective inductance of the planes. Such a via has to go through a via hole in a plane having a different dc level in order to avoid a short circuit. Through this via and via hole, fields in different plane pairs get coupled to each other.
In addition, planes often have irregular geometries. There can be large apertures and splits in planes. Fields in different plane pairs can get coupled through these apertures. This can be regarded as a coupling by means of a wrap-around current on the edges of the planes. For narrow slots, a transmission-line-based model has been proposed to take into account this interlayer coupling. Electric and magnetic polarization currents have also been considered to compute the coupling through electrically small cutouts.
The field penetration through the conductors can be neglected for frequencies, where the skin depth is much smaller than the plane thickness. At lower frequencies, this field penetration has to be taken into account. For purposes of the description presented below, the thickness of the metal is assumed to be much larger than the skin depth. This assumption is valid above several megahertz for commonly used copper planes in packages.
Based on the finite-difference method (FDM), two equivalent circuit models for power and ground planes have been developed: T- and X-models. The multilayered FDM (MFDM) provides a simpler approach without any limit on the number of layers. It provides an accurate representation of wrap-around currents in complicated geometries, which have not been modeled before.
The multi-layered finite-difference method (M-FDM) is a finite difference-based technique that can solve power plane problems using square-meshes. The limitation of the method is that it uses a rigid, square, grid. Typically, package PDNs are electrically large. Thus, for a large solid plane, the square mesh used by MFEM can use a cell size that is dependent on the maximum frequency of simulation. A good rule of thumb is to use a discretization width of λ/20. However, these PDNs also contain geometrically small features such as split planes and apertures. To capture very fine structures, the regular mesh becomes dense locally and globally, resulting in a large number of unknowns.
In typical package geometries, the minimum feature size can easily be less that 100 μm or 4 mils. Thus for a 50 mm×50 mm package, the total number of cells required to model one solid plane-pair using a 100 μm cell size is 250,000. Although M-FDM has been demonstrated in its current implementation for a maximum of 1 million unknowns, this only allows for the modeling of four plane-pairs. Given that the feature size on package and board are shrinking to allow for greater wiring density, the mesh is a serious limitation of M-FDM.
It would be desirable to have methods and software that may be used to model multilayer planes and provide equivalent circuit models for such structures in which non-uniform meshes are used to model circuit equivalents in a power or ground plane.